Psyc 60 Regression

# Psyc 60 Regression - Regression Prediction If there is a correlation between two variables then from a person's score on one variable we can do

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Regression

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Prediction If there is a correlation between two  variables, then from a person’s score on  one variable, we can do better than  chance in predicting that person’s score  on the other variable.
An example…

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Scatter Plot What is the relationship between level of education and lifetime  earnings? Education Level and Lifetime Earnings 0 1 2 3 4 5 0 2 4 6 8 10 Education (Predictor Variable) Lifetime Earnings (Criterion Variable) Intuitively, draw  the best fitting  line through the  data so that  roughly half the  points are  above the line  and half the  points are below  the line.
Line of Best Fit If it is reasonable to assume that X and  Y are linearly related, we can improve  our prediction of Y from X by finding the  straight line of best fit to the Y values.

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Cartesian Coordinate System
Cartesian Coordinate System

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Cartesian Coordinate System Y = (m)(X) + b b = y intercept m = slope = rise/run
Least Squares Regression Equation The least squares regression equation  is used to predict Y scores from X  scores. a X b Y + = ) )( ( ˆ 0) X (when intercept Y (rise/run) slope variable predictor variable criterion y, of value predicted the , hat" y " ˆ = = = = = a b X Y r S S b x y = ) )( ( X b Y a - = Note  uppercase  “S”.

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An Example: Regression What is the relationship between level of education and lifetime  earnings? a X b Y + = ) )( ( ˆ r S S b x y = 29 . 2 8 ) 36 ( ) 204 ( 8 2 2 = - = x S 10 . 1 8 ) 7 . 17 ( ) 83 . 48 ( 8 2 2 = - = y S 43 . ) 90 (. 29 . 2 10 . 1 = = b X Education Y Income XY X 2 Y 2 8 3.4 27.2 64 11.56 7 4.4 30.8 49 19.36 6 2.5 15 36 6.25 5 2.1 10.5 25 4.41 4 1.6 6.4 16 2.56 3 1.5 4.5 9 2.25 2 1.2 2.4 4 1.44 1 1 1 1 1 36 17.7 97.8 204 48.83
An Example: Regression 43 . ) 90 (. 29 . 2 10 . 1 ) ( = = = r S S b x y a X b Y + = ) )( ( ˆ r S S b x y = ) )( ( X b Y a - = 27 . ) 50 . 4 ( 43 . 21 . 2 ) )( ( = - = - = X b Y a 27 . 43 . ˆ + = X Y 50 . 4 21 . 2 = = X Y

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An Example: Regression How much money in lifetime earnings would a person make  who has an education level of 6? Education Level and Lifetime Earnings y = 0.4321x + 0.2679 0 1 2 3 4 5 0 2 4 6 8 10 Education (Predictor Variable) Lifetime Earnings (Criterion Variable) X (Education) Y (Income) 8 3.4 7 4.4 6 2.5 5 2.1 4 1.6 3 1.5 2 1.2 1 1 000 , 850 , 2 \$ 85 . 2 27 . ) 6 ( 43 . ˆ
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## This note was uploaded on 01/30/2009 for the course PSYC 60 taught by Professor Ard during the Spring '08 term at UCSD.

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Psyc 60 Regression - Regression Prediction If there is a correlation between two variables then from a person's score on one variable we can do

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